Boltzmann Medal

Toward StatPhys 2025.

Interview with Yoshiki Kuramoto, Kyoto University (Japan)

By Franco Bagnoli, University of Florence and Caffè-Scienza Association (Italy)

Prof. Kuramoto, could you begin by sharing a bit about your educational background and the formative experiences that steered your interest toward statistical physics and nonlinear dynamics?

I was a student of theoretical physics. My dissertation was about the theory of second-order phase transitions. Since my graduate school days, I had been somewhat interested in the phenomenon of far from equilibrium, partly due to the influence of my supervisor. A few years after I obtained my doctorate, around 1973, I read the book “Thermodynamic theory of structure, stability and fluctuations” by P. Glansdorff and I. Prigogine, and since then I have been involved in the study of self-organization phenomena of non-equilibrium open systems. Also, at that time, the wave patterns of the Belousov-Zhabotinsky reaction system, known as the oscillatory chemical reaction, were attracting a lot of interest from researchers, which may have been one of the factors that led me to study oscillation and kinetic phenomena. I think that at that time, the whole academic community was expecting and accepting the emergence of the field of nonlinear dynamics.

One of your most significant contributions, the Kuramoto model, has found remarkable applications across a vast spectrum of scientific disciplines, extending beyond physics and mathematics to chemistry, biology, neuroscience, physiology, complex networks, and various engineering fields. Could you elaborate on the genesis of this work and what factors you believe have contributed to its profound and widespread influence?

The idea for the now-called Kuramoto model, came from a chance encounter with A. Winfree’s 1967 paper Biological rhythms and the behavior of populations of coupled oscillators. It was already seven years after the paper was published, but I was introduced to it by a colleague in the biology department who was interested in circadian rhythms. Since I had a background in phase transition theory, I was shocked to learn that a completely new dynamic phase transition phenomenon called synchronization phase transition could exist. I was also impressed by how Winfree treated a mathematically difficult object (the limit cycle oscillator) with only one variable, the phase, thereby opening the way to theoretically treat the collective dynamics of oscillators.

My model was created from the desire to somehow transform Winfree’s model into a model that could be solved analytically. I never imagined that it would attract the interest in such a wide range of fields as it is today. Therefore, I was very surprised and happy when I learned of the paper by K. Wiesenfeld et al. that revealed that my model can be applied to superconducting Josephson arrays. Perhaps it is a minimal model for mathematically describing the synchronization phase transition. I think that this and the good symmetry of this model are fortunate in that they provide room for various modifications and generalizations.

Could you share insights into how collaborations and interactions with fellow scientists and your students have shaped the trajectory of your research?

When I published the Kuramoto model, I was also working on pattern dynamics of oscillatory reaction-diffusion systems. My most important collaborator, T. Yamada, was a friend from my undergraduate days at the same university, and I remember that our research progressed rapidly together. At the time, I was in a low position as a researcher, but I had few chores and was in a favorable environment where I could freely conduct research according to my interests. Even after I became a professor, unlike now, there was not much pressure to always produce short-term results, and I was not required to spend much time on paperwork and other things to obtain research funds, so I had plenty of time to discuss with students and was able to receive a lot of inspiration from them.

I was also fortunate to be able to concentrate on my research in an atmosphere that was tolerant of my research, even though it was different from traditional physics, even though I was affiliated with the Physics Department for most of my active years.

You were recently honored with the Boltzmann Medal. Could you reflect on the significance of this prestigious award in the context of your career and the broader field?

Past recipients of this award include many researchers whom I have looked up to in the past, so I felt very honored to have my name written alongside them. As I am the third recipient in Japan after R. Kubo and K. Kawasaki, I hope that this award will encourage many researchers in our country, especially young researchers in statistical physics. I am also very pleased that the theory of coupled oscillator dynamics and synchronization phenomena has been publicly recognized as part of statistical physics. I think this is also good news for researchers in the field of nonlinear dynamics, which includes this topic.

Looking to the future, what emerging or underexplored avenues do you see as particularly promising for productive research in statistical physics and nonlinear dynamics?

Most predictions about the future will be wrong. Innovation often appears suddenly and unexpectedly from obscure places. Moreover, I do not have enough knowledge or experience to look at these academic fields as a whole. If I may express my expectations for the future within the scope of my interests, I believe that there is a lot of room for statistical physics and nonlinear dynamics to contribute in relation to biological phenomena. Modern life science has made amazing progress in terms of molecular mechanisms, but research from the standpoint of statistical mechanics or dynamics is lagging far behind. For example, in the process of evolution of life, living things have adopted any dynamic mechanism that can be used for survival. In relation to my research, I think the dynamic mechanism of synchronization is the most prominent example of such a mechanism. I think modern technology can also learn a lot by better understanding how ingeniously life uses such mechanisms.